Rumors' spread: A game theoretical approach with the replicator dynamics

Elvio Accinelli; Luis Quintas; Humberto Muñiz

doi:10.3934/jdg.2022020

Article Contents

2023, Volume 10, Issue 1: 11-23. Doi: 10.3934/jdg.2022020

This issue Previous Article On the symmetry relation between different characteristic functions for additively separable cooperative games Next Article Discrete approximation of stationary Mean Field Games

Rumors' spread: A game theoretical approach with the replicator dynamics

1.
Facultad de economía de la Universidad Autónoma de San Luis Potosí, México
2.
Departamento de Matemática de La Universidad Nacional de San Luis, Argentina
3.
Instituto Potosino de Investigación Científica y Tecnológica, México

^*Corresponding author: Humberto Muñiz
^*Corresponding author: Humberto Muñiz

Received: March 2022

Revised: August 2022

Early access: September 2022

Published: January 2023

The authors wish to thank the anonymous referees for the helpful comments and constructive remarks on this manuscript.

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Abstract

In this paper we study a repeated game and the replicator dynamics to analyze the spread of a rumor in a society formed by two populations. One population is informed about a rumor and communicates the rumor to the other population. According to the preferences of each individual, this rumor is communicated in its original or in a modified form. We analyze the stability of dynamic equilibria. We conclude that there are three possibilities for the spread of a rumor. The rumor may end up being disseminated in its original version or being distorted by the diffusers throughout the society, or a part of the population remains in the long term spreading the rumor in its original form and another in a distorted way.

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Mathematics Subject Classification: Primary: 91A05, 91A22; Secondary: 91A25.

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Figure 1. The phase diagram for the dynamics of the rumors

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Table 1. Payoff matrix

$ I\downarrow/NI\rightarrow $	$ O $	$ D $
$ O $	$ a, \; b $	$ -c, \;-d $
$ D $	$ -e, \;-f $	$ g , \;h $

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